Ultrasonic energy transmission in rectilinear array scanning patterns of soft tissue provides projection density values of the tissue which are recorded as a function of scanning position and angular relationship, .theta., of the subject with a fixed coordinate system. A plurality of rectilinear scan arrays in the same plane for different angular relationships .theta..sub.1 . . . .theta..sub.n thus recorded are superimposed. The superimposition of intensity values thus yields a tomographic image of an internal section of the tissue in the scanning plane.